For Toolbox parts we usually use on configuration name in bom
"User specified name".
Is there any method to obtain this value and to use it in PDMWE
BOM.
For the toolbox parts we want to use this value not the
configuration name.

I don't think PDMWE supports the "User specified name" at
this time, it is not a standard custom property. If you look at the
stock BOM that comes with SolidWorks for drawings the "User
specified name" is the Part Number property, and custom properties
are listed separatly when setting what property to show for a BOM
colum. You may want to conact your SolidWorks reseller and have
them write a script to copy the "User specified name" to a custom
property like PartNo so you can use it in PDMWE
Erik